Problem: Simplify the following expression: $z = \dfrac{1}{10y} - \dfrac{7}{8y}$
Explanation: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10y$ and $8y$ $\lcm(10y, 8y) = 40y$ $ z = \dfrac{4}{4} \cdot \dfrac{1}{10y} - \dfrac{5}{5} \cdot \dfrac{7}{8y} $ $z = \dfrac{4}{40y} - \dfrac{35}{40y}$ $z = \dfrac{4 -35}{40y}$ $z = \dfrac{-31}{40y}$